Least Common Multiple (LCM) of 137 and 79
The least common multiple (LCM) of 137 and 79 is 10823.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 137 and 79?
First, calculate the GCD of 137 and 79 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 79 = 1 remainder 58 |
| 2 | 79 ÷ 58 = 1 remainder 21 |
| 3 | 58 ÷ 21 = 2 remainder 16 |
| 4 | 21 ÷ 16 = 1 remainder 5 |
| 5 | 16 ÷ 5 = 3 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 79 | 10428 |
| 182 and 128 | 11648 |
| 55 and 40 | 440 |
| 164 and 77 | 12628 |
| 67 and 157 | 10519 |